Solve 2ab^2+15a^2b+3?

$$2 a b ^ { 2 } + 15 a ^ { 2 } b + 3 ?$$

Differentiate w.r.t. a

$$2b\left(15a+b\right)$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2b^{2}a^{1-1}+2\times 15ba^{2-1}$$

Subtract 1 from 1.

$$2b^{2}a^{0}+2\times 15ba^{2-1}$$

Multiply 2 times 15b.

$$2b^{2}a^{0}+30ba^{2-1}$$

Subtract 1 from 2.

$$2b^{2}a^{0}+30ba^{1}$$

For any term t, t^{1}=t.

$$2b^{2}a^{0}+30ba$$

For any term t except 0, t^{0}=1.

$$2b^{2}\times 1+30ba$$

For any term t, t\times 1=t and 1t=t.

$$2b^{2}+30ba$$

Evaluate

$$2ab^{2}+15ba^{2}+3$$